The photon structure function, in quantum field theory, describes the quark content of the photon. While the photon is a massless boson, through certain processes its energy can be converted into the mass of massive fermions. The function is defined by the process e + γ → e + hadrons. It is uniquely characterized by the linear increase in the logarithm of the electronic momentum transfer log Q2 and by the approximately linear rise in x , the fraction of the quark momenta within the photon. These characteristics are borne out by the experimental analyses of the photon structure function.
Theoretical basis Photons with high photon energy can transform in quantum mechanics to lepton and quark pairs, the latter fragmented subsequently to jets of hadrons, i.e. protons, pions, etc. At high energies E the lifetime t of such quantum fluctuations of mass M becomes nearly macroscopic: t ≈ E/M2; this amounts to flight lengths as large as one micrometer for electron pairs in a 100 GeV photon beam, while even for light hadrons the length is on the order of 10 fermi, i.e. 10x the radius of a proton. High energy photon beams have been generated by photon radiation off electron beams in e−e+ circular beam facilities such as PETRA at DESY in Hamburg and LEP at CERN in Geneva. Exceedingly high photon energies may be generated in the future by shining laser light on teraelectronvolt electron beams in a linear collider facility. The classical technique for analyzing the virtual particle content of photons is provided by scattering electrons off the photons. In high-energy, large-angle scattering the experimental facility can be viewed as an electron microscope of very high resolution Q, corresponding to the momentum transfer in the scattering process according to Heisenberg's uncertainty principle. The intrinsic quark structure of the target photon beam is revealed by observing characteristic patterns of the scattered electrons in the final state.
The incoming target photon splits into a nearly collinear quark–antiquark pair. The impinging electron is scattered off the quark to large angles, the scatter pattern revealing the internal quark structure of the photon. Quark and antiquark finally transform to hadrons. Photon structure function can be described quantitatively in quantum chromodynamics (QCD), the theory of quarks as constituents of the strongly interacting elementary particles, which are bound together by gluonic forces. The primary splitting of photons to quark pairs, cf. Fig. 1, regulates the essential characteristics of the photon structure function, the number and the energy spectrum of the quark constituents within the photon. QCD refines the picture by modifying the shape of the spectrum, to order unity unlike the small modifications naively expected as a result of asymptotic freedom. Quantum mechanics predicts the number of quark pairs in the photon splitting process to increase logarithmically with the resolution Q, and (approximately) linearly with the momenta x. The characteristic behavior
F 2 , B γ ( x , Q 2 ) = f B ( x ) log Q 2 / Λ 2 + . . . {\displaystyle F_{2,B}^{\gamma }(x,Q^{2})=f_{B}(x)\log {Q^{2}/\Lambda ^{2}}+...}
with
f B ( x ) = 3 α 2 π ∑ q , q ¯ e q 4 x [ x 2 + ( 1 − x ) 2 ] {\displaystyle f_{B}(x)={\frac {3\alpha }{2\pi }}\sum _{q,{\bar {q}}}e_{q}^{4}x[x^{2}+(1-x)^{2}]}
is predicted for the photon structure function in the quark model to leading logarithmic behavior; where α is the fine-structure constant and the fractional quark charges are denoted eq; with the factor 3 accounting for the quark color degrees. Turning on the radiation of gluon quanta off quarks in QCD, the quark momenta are reshuffled partly from large to small x values with increasing resolution. At the same time the radiation is damped moderately due to asymptotic freedom. The delicate interplay between photon splitting and damped gluon radiation re-normalizes the photon structure function
F 2 , B γ ( x , Q 2 ) → F 2 γ ( x , Q 2 ) = f ( x ) log Q 2 / Λ 2 {\displaystyle F_{2,B}^{\gamma }(x,Q^{2})\rightarrow F_{2}^{\gamma }(x,Q^{2})=f(x)\log {Q^{2}/\Lambda ^{2}}}
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